# This Source Code Form is subject to the terms of the Mozilla Public
# License, v. 2.0. If a copy of the MPL was not distributed with this
# file, You can obtain one at https://mozilla.org/MPL/2.0/.
import sisl as si

# Generate square lattice with nearest neighbor couplings
square = si.Geometry([[0.5, 0.5, 0]], lattice=si.Lattice([1, 1, 10], [3, 3, 1]))

# Generate Hamiltonian
H = si.Hamiltonian(square)

# Show the initial state of the Hamiltonian
print(H)

# Specify matrix elements (on-site and coupling elements)
H[0, 0] = -4.0
H[0, 0, (1, 0)] = 1.0
H[0, 0, (-1, 0)] = 1.0
H[0, 0, (0, 1)] = 1.0
H[0, 0, (0, -1)] = 1.0

# Show that we indeed have added some code
print(H)

# Create band-structure for the supercell.
band = si.BandStructure(H, [[0.0, 0.0], [0.5, 0.0], [0.5, 0.5], [0.0, 0.0]], 300)

# Calculate eigenvalues of the band-structure
eigs = band.apply.ndarray.eigh()

# Plot them
import matplotlib.pyplot as plt

plt.figure()
plt.title("Bandstructure of square, nearest neighbor")
plt.xlabel("k")
plt.ylabel("Eigenvalue")

# Generate linear-k for plotting (ensures correct spacing)
lband = band.lineark()
for i in range(eigs.shape[1]):
    plt.plot(lband, eigs[:, i])
plt.savefig("05_square_bs.png")